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The quantum description and stimulated emission radiation of coupled metamaterials

In recent years, there has been increasing interest in studying the quantum characteristics in plasmonic metamaterials. By using the Hamiltonian combined with second quantization, we have investigated the basic excitation of the coupled metamaterials and presented a quantum description of them. The interaction between the excitation of the coupled metamaterial and the exciton in the quantum dot material has been further considered with the aid of the interaction Hamiltonian. In such a damping system, a set of Langevin equations has been used to deal with the quantum motion of the system. And the stimulated emission has been found, which can be used to form a nano-laser. The quantum description of coupled metamaterial and the interaction system could work as the fundamental method in paving the way for studies on quantum effects in coupled metamaterials.